Yoav Levy PHD Thesis - innovative techniques for US imaging

INVESTIGATION OF NEW TECHNIQUES FOR ULTRASONIC
IMAGING
Research Thesis
In Partial Fulfilment of the
Requirements for the
Degree of Doctor of Philosophy
Yoav Levy
Submitted to the Senate of
the Technion - Israel Institute of Technology
Adar, 5767 Haifa February 2007

ACKNOWLEDGMENTS
The research thesis was done under the supervision of Dr. Haim Azhari of the Faculty of
Bio-Medical Engineering, Technion. Ass/Prof Yehuda Agnon of the faculty of Civil and
Environmental Engineering, Technion, served as an adviser.
The generous financial help of the Technion is gratefully acknowledged.

CONTENTS
ACKNOWLEDGMENTS
CONTENTS
LIST OF FIGURES
ABSTRACT 1
GLOSSARY 3
INTRODUCTION 4
ULTRASONIC IMAGING 4
Imaging Methods 4
Velocity Estimation 6
Bio-Effects 6
SPEED OF SOUND DISPERSION 7
CODED EXCITATION 8
OBJECTIVES AND OUTLINE OF THE THESIS 10
OBJECTIVE 10
THESIS OUTLINE 10
METHODS 13
PAPER A: "MEASUREMENT OF SPEED OF SOUND DISPERSION
IN SOFT TISSUES USING A DOUBLE FREQUENCY CONTINUOUS
WAVE METHOD" 13
PAPER B: "ULTRASONIC SPEED OF SOUND DISPERSION
IMAGING" 40
PAPER C: "SPEED OF SOUND DISPERSION MEASUREMENT
USING A CHIRP SIGNAL" 61
PAPER D: "VELOCITY MEASUREMENTS USING A SINGLE
TRANSMITTED LINEAR FREQUENCY MODULATED CHIRP" 85
PAPER E: "A METHOD FOR LOCAL SPECTRAL ANALYSIS
USING CODED EXCITATIONS AND ITS APPLICATION IN
VELOCITY ESTIMATION" 102
DISCUSSION 118
CONTRIBUTIONS 118
FUTURE WORK 124
CONCLUSIONS 125
REFERENCES 126

LIST OF FIGURES
Figure 1 – a sample of a long burst comprising of two
frequencies, one being the double that of the other 119
Figure 2 – A sample of a linear frequency modulated signal
(Chirp). 119
Figure 3 - The speed of sound dispersion index versus the
average frequency for the turkey breast (left) and bovine
heart (right). The error bars correspond to the 95%
confidence level range. 121
Figure 4 – A schematic illustration of the setup used for
measurement of SOSD in soft tissue using pulse-echo
mode. 123

1
ABSTRACT
Ultrasonic imaging offers a valuable non-invasive diagnostic tool. The purpose of this study
was to investigate new techniques for ultrasonic imaging in order to: (a) Introduce a new
ultrasonic imaging contrast which may contribute to tissue characterization and tumour
detection. (b) Improve the performance of current methods. The chosen strategy to achieve
both challenges was to combine novel spectral analysis methods with the transmission of
special signals.
While most imaging techniques have focused on dominant properties such as tissue
echogenity and attenuation, speed of sound dispersion (SOSD) phenomenon is very weak
and difficult to measure, and hence has not been used for imaging. In this study, three new
methods for measuring SOSD which are sensitive for the weak dispersion in soft tissues are
introduced. Using the new techniques, SOSD is utilized as a new imaging contrast source.
Spectral analysis applied to backscattered ultrasound signals is used in many applications
such as attenuation mapping, tissue characterization, temperature monitoring and mean
scatterer spacing estimation. Furthermore, it plays a major role in velocity estimation since
velocity is associated with the frequency dependant Doppler shift. Signal to noise ratio
(SNR) is a great concern in such applications. Hence, it is desirable to utilize high energy
transmitted signals. The signal energy can be augmented by increasing the intensity of the
transmitted signal. However, this approach is limited by safety aspects. Alternatively, one
can increase the transmission duration, but this approach commonly decreases the axial
resolution. A method for performing localized spectral analysis using long structured
signals was developed.
In this study, it was shown that the combination of long structured signals and appropriate
algorithms yields benefits in terms of SNR, measurement accuracy and acquisition rate.
With respect to the measurement of SOSD, this study has clearly demonstrated the
feasibility of SOSD projection imaging and that SOSD may serve as a new contrast source.
Images, based on SOSD projections, and measurements of SOSD in soft tissues in pulse-
echo mode were presented for the first time. These new imaging techniques may contribute

2
to tissue characterization, tumour detection and breast diagnosis. One of the methods
developed for SOSD measurement was also found suitable for estimation of target velocity
in single ultrasonic transmission.

3
GLOSSARY
Abbreviations
A-Mode Amplitude Mode
B-Mode Brightness Mode
CT Computed Tomography
M-Mode Motion mode
SNR Signal to Noise Ratio
SOSD Speed of sound dispersion
TOF time of flight
TFR Time frequency representation
2D Two-dimensional
3D Three-dimensional

4
C h a p t e r 1
INTRODUCTION
This chapter is an overview of research areas which are related to this study.
Ultrasonic Imaging
In ultrasonic imaging, image formation is obtained by analysing ultrasonic waves passing
through an object. In this context, ultrasound is the mechanical vibration of matter with
frequencies above 20 kHz: above audible sound. Ultrasonic imaging methods are divided
into two families, “pulse-echo” and “transmission”. The pulse–echo method depends on the
emission of a pulse of ultrasound and the reception of its echo from an imaged target. The
transmission method is based on the measurement of a transmitted pulse after passing
through an imaged object.
Imaging Methods
A variety of imaging methods are derived from the two major imaging techniques.
A-Mode
The "A" in A-mode stands for "amplitude". The amplitude of an ultrasonic pulse reflected
from tissue structures along the beam path are presented on a display. The range from
which the echoes are reflected can be calculated from the time that has elapsed between the
pulse transmission and the reception of the echoes, given the wave propagation speed. This
type of information which is obtained for the beam path is referred to as A-line.
B-Mode
B-Mode is similar to A-mode, but the amplitude of reflected sound is displayed as
brightness along a one dimensional line which corresponds to time.
The A-mode and B-mode techniques are now used infrequently in medical imaging, but
they are the basic building blocks for the more advanced modes, currently used.

5
M-Mode
The M-Mode consists of a series of B-Mode lines displayed side-by-side so that movements
of tissues along the beam path can be traced. A high repetition rate of the measurements is
the advantage of this method and therefore it is still used for cardiac imaging.
B-Scan
B-Scan is a two-dimensional real time imaging method which is used to create a cross-
sectional view of imaged organs. The 2D images are formed out of sequential A-lines
(presented using brightness mode) which are obtained while sweeping the ultrasonic beam
to cover the imaged area. This is the most used ultrasonic imaging mode. Usually, the
measurements of other modes, if used, are presented on top of the B-Scan image. The
images are acquired with a high frame rate of up to 100 frames per second.
3D and 4D imaging
Three-dimensional (3D) ultrasonic images are obtained by compounding two-dimensional
B-Scan images. In modern ultrasonic devices, the 3D images are acquired fast enough to be
presented sequentially at several images per second. The term 4D imaging stands for
displaying 3D images as function of time, the fourth dimension.
Transmission
The transmission imaging method is based on measurements of an ultrasonic pulse which
has passed through an object. In this method a projection of the imaged object is obtained.
Depending on the signal generation and analysis used, different properties of the imaged
object can serve as the source of contrast for the projection. Projections of the absorption in
the imaged object are obtained by measurement of the amplitude of the received signal.
Projections of the speed of sound in the imaged object are obtained by measuring the total
time of flight (TOF) of the transmitted signal.
Ultrasonic Computed Tomography
Cross sectional images are formed out of multiple projections acquired from different
angles around the object and by using standard CT reconstruction algorithms. Projections of
the speed of sound and projections of the absorption in the imaged object can serve as the
source of contrast for the tomographic reconstruction.

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Velocity Estimation
The Doppler Effect is named after an Austrian physicist Johann Christian Doppler. In
ultrasonic Doppler measurements, the change in a received frequency is used to estimate a
target’s velocity. This frequency shift is due to the relative motion between the sound
source and the reflecting target.
Continuous-wave Doppler
In continuous wave Doppler, two different transducers are used: one to send and the other
to receive a continuous harmonic signal. The velocity of the target is estimated out of the
frequency difference between the sent and received signals. In this method the depth of the
moving target can not be resolved.
Pulse-echo Doppler
Pulse-echo Doppler systems were developed in order to resolve the range from which the
ultrasonic beam is reflected by the moving target (e.g. blood). A single transducer is used to
transmit several pulses into the tissue and receive their reflections (A-lines). The movement
of the blood in the tissue causes changes in the A-lines. The velocity of the blood at a
certain tissue depth is estimated by analysing the variations in the A-lines at the
corresponding time delays (relative to pulse emission). The evolution of the power density
spectrum of the detected velocities as function of time is displayed as a sonogram.
Color Doppler
Color Doppler is a technique for displaying a map of blood flow in real-time. The velocity
estimation for multiple ranges and directions results in a flow map that is presented on top
of the B-scan image. The flow direction and mean velocity are designated by color and the
image brightness corresponds to the magnitude of the flow (Behar et al. 2003).
Power Doppler
In power Doppler, the total integrated Doppler power is displayed in color. This allows
better visualization of small vessels at the sacrifice of the velocity information.
Bio-Effects
Ultrasound imaging is considered to be a hazardless imaging modality. There is no doubt
that the diagnostic ultrasonic radiation is safer than X-ray radiation and that it is safer than
the radioisotopes which are used in other imaging modalities such as SPECT and PET.

7
However, ultrasonic imaging involves the transmission of energy to the body and this
energy has two major bio-effects: it may cause thermal heating and cavitation (Sheiner et al.
2007).
The temperature of a tissue may be raised by ultrasonic radiation, especially in places where
the ultrasonic absorption is high such as bone surfaces. Doppler ultrasound is more likely to
cause tissue heating than simple imaging since it utilizes many more transmissions per
second and they are targeted towards small regions. The thermal index (TI) is an indication
of the potential tissue temperature rise for three types of tissues. TIS is an index used to
provide an estimate for soft tissue exposures. TIB is used for bones close to the beam focus.
TIC is the cranial-bone thermal index (O’Brien et al. 1999). High energy ultrasonic beams
are utilized to cause tissue heating for therapeutic purposes.
Cavitation is the formation of transient or stable bubbles. The bubbles grow and then
contract due to the ultrasonic field. They may collapse causing instantaneous bursts of very
high temperatures and pressures, which are potentially harmful. The existence of gas in the
tissue being imaged increases the probability for cavitation. Therefore the danger of
cavitation is relatively higher in tissues that contain gas bodies, such as tissues of the lung
or intestine and tissues with artificial micro-bubbles (a contrast agent).
There are other bio-effects that should be considered when discussing ultrasonic radiation.
(a) In the presence of liquids, the ultrasonic beam may cause acoustic streaming which
potentially can cause shearing near solid objects and that may lead to thrombosis. (b)
Ultrasonic radiation force may cause electrical changes in cell membranes (Nyborg 2002).
Speed of Sound Dispersion
Speed of sound dispersion (SOSD) refers to the phenomenon of the change of speed of
sound with frequency. SOSD is very weak in soft tissues and was considered negligible in
medical imaging (Wells 1999). Hence, the measurement of the SOSD is considered more
difficult than the measurement of other acoustical properties such as attenuation (He 1999).
It has been suggested by O'Donnell et al. (1981) that the SOSD in an unbounded medium is
connected to the attenuation by the "Kramers-Kronig" relationship. They also derived
useful approximations for this relation.

8
The measurement of speed of sound dispersion in nonbiological substances was done by
several researchers. Wolfgang and Yih-Hsing (1978) measured the dispersion in dispersive
solids. Chin et al. (1990) and He (1999) measured the dispersion in highly-attenuating
specimens in order to verify the Kramers-Kronig relationship for acoustic waves. Lang et
al. (2000) measured the dispersion in nanocrystalline materials.
Few investigators have studied the speed of sound dispersion in biological tissues. Kremkau
et al. (1981) measured the speed of sound dispersion in normal brain tissue. Wear (2000),
Strelitzki and Evans (1996) and Droin et al (1998) measured the dispersion in bones.
Pedersen and Ozcan (1986) measured the dispersion in lung tissues. Carstensen and
Schwan (1959) measured acoustic properties of hemoglobin solutions including dispersion.
Recently, Marutyan et al (2006) have studied the SOSD in myocardial tissue.
Coded Excitation
The signal to noise ratio (SNR) is a great concern in ultrasonic applications. Hence, it is
desirable to utilize high energy transmitted signals. The signal energy can be augmented by
increasing the intensity of the transmitted signal. However, this approach is limited by
safety aspects. Alternatively, one can increase the transmission duration since in most of the
medical imaging systems the average power delivered to the imaged tissue is significantly
lower than the maximum allowed radiation level (M. O‘Donnell 1992), but this approach
commonly decreases the axial resolution.
An approach for utilizing long signals without sacrificing the axial resolution is the
implementation of coded excitation (Misaridis and Jensen 2005, Behar 2004). With this
approach, a long coded signal such as a chirp is used to transmit high energy while
preserving low intensity constraints. Using coded signals, the spatial resolution can be
recovered with an appropriate compression algorithm, such as matched filter techniques
(Pollakowski and Ermert 1991). The concept of using coded excitation was borrowed from
other modalities (e.g. radar, Soumekh 1999).
Frequency modulated excitation codes have been considered for ultrasonic imaging as well
as binary codes, such as Golay sequences. The Golay sequences are used in pairs for
sidelobes cancellation (Bae et al. 2002). In a thorough study, Misaridis and Jensen (2005a,

9
2005b and 2005c) conclude that frequency modulated signals have the best performance in
ultrasonic imaging. However, other codes are used in some imaging systems.

10
C h a p t e r 2
OBJECTIVES AND OUTLINE OF THE THESIS
This chapter states the objectives of the research and sketches its outline.
Objective
Ultrasonic imaging offers a valuable non-invasive diagnostic tool. The purpose of this study
was to investigate new techniques for ultrasonic imaging in order to: (a) Introduce a new
ultrasonic imaging contrast which may contribute to tissue characterization and tumour
detection. (b) Improve the performance of current methods. The chosen strategy to achieve
both challenges was to combine novel signal analysis methods with the transmission of
special coded signals.
Thesis outline
This thesis is comprised of five papers (A-E), three of them were accepted for publication
and the two others have been submitted.
Paper A: "Measurement of Speed of Sound Dispersion in Soft Tissues Using a Double
Frequency Continuous Wave Method"
While most ultrasonic imaging techniques have focused on dominant properties such as
tissue echogenity, speed of sound and attenuation. The speed of sound dispersion (SOSD)
phenomenon is very weak and difficult to measure, and hence has not been used for
imaging. In this paper, a novel method for measuring the speed of sound dispersion is
introduced. The method combines a short pulse transmission followed by a long burst
comprising of two frequencies, one being the double that of the other. In the paper, the
method is validated by measurement of SOSD in plastic samples. Then the applicability of
the method for usage in soft tissues is tested by measurements of SOSD in in-vitro soft
tissues samples. The significance of the difference in the speed of sound dispersion index

11
between the studied materials is checked to confirm the potential of SOSD to be used as a
new index for soft tissue characterization by ultrasound.
Paper B: "Ultrasonic Speed of Sound Dispersion Imaging"
In paper B, the feasibility for speed of sound dispersion (SOSD) imaging was investigated.
Using a through transmission mode, the method which was introduced in paper A for
SOSD measurement, was utilized. SOSD projection images which were obtained by
scanning objects immersed in water using a raster mode utilizing a computerized scanning
system are presented. Using this approach SOSD projection images were obtained for
solids and fluids as well as for a tissue mimicking breast phantom and an in-vitro soft
tissues phantom. The results obtained in the paper, have clearly demonstrated the feasibility
of SOSD projection imaging.
Paper C: "Speed of Sound Dispersion Measurement Using a Chirp Signal"
In the study covered in paper C, two new methods for speed of sound dispersion
measurement were developed. The main advantage of these methods is the ability to
measure SOSD in the pulse-echo mode in soft tissues. These methods are based on the
transmission of a linear frequency modulated “chirp” pulse. The first method, entitled as the
“signals bank method" is based on assessment of similarity between the measured signal
and a synthesized bank of signals. The second method, titled the "cross correlation method"
is computationally faster and is based on the calculation of the phase of the peak of the
complex cross correlation function. The performance of the methods in terms of robustness
and computational effort are compared in the paper. To the best of our knowledge, SOSD
measurements in the pulse-echo mode in soft tissues are published for the first time in this
paper.
Paper D: "Velocity Measurements Using a Single Transmitted Linear Frequency
Modulated Chirp"

12
In paper D, a new method for velocity estimation using a single linear frequency modulated
chirp transmission is presented and implemented for ultrasonic measurements. The method
is based on the calculation of the complex cross correlation function between the
transmitted and reflected signals. The velocity is then calculated from the phase of the peak
of the envelop of this cross correlation function. In this paper, the suggested method was
verified using computer simulations and experimental measurements in an ultrasonic
system.
Paper E: "A Method for Local Spectral Analysis Using Coded Excitations and its
Application in Velocity Estimation"
In paper E, a method for performing localized spectral analysis is suggested. The method is
based on transmitting a long frequency modulated signal. The frequency dependent
information of the detected backscattered waves is obtained by using a time frequency
transform such as the short time Fourier transform (STFT). The spatial resolution is
retrieved by the rearrangement of the frequency-time relationship of the signal.
In this paper, a simulation program was used to confirm the ability of this method to serve
as a tool for velocity estimation. The simulated echoes reflected from a moving target after
the transmission of a long chirp signal were analyzed. The performance of the suggested
method was compared to a conventional method for velocity estimation.

13
C h a p t e r 3
METHODS
Paper A: "Measurement of Speed of Sound Dispersion in Soft Tissues Using a Double
Frequency Continuous Wave Method"
Abstract
A method for measuring the speed of sound dispersion is introduced. The method
combines a short pulse transmission followed by a long burst comprising of two
frequencies, one being the double that of the other. The method allows the determination of
the speed of sound dispersion using a single transmission. To validate the method, the
dispersion was first measured in plastic samples and then in in-vitro soft tissues samples.
The results obtained for perspex samples are in excellent agreement with values reported in
the literature. The dispersion index in soft tissues ranged for a bovine heart from 0.63 ±
0.24 (m/sMHz) at 1.5 MHz to 0.27 ± 0.05 (m/sMHz) at 4.5 MHz and for a turkey breast
from 1.3 ± 0.28 (m/sMHz) at 1.75 MHz to 0.73 ± 0.1 (m/sMHz) at 3.8 MHz. The

14
significant difference in the speed of sound dispersion index between the studied materials
indicates that dispersion may be used as a new index for soft tissue characterization by
ultrasound.
Keywords: Ultrasound, Speed of sound, Dispersion, Tissue characterization.

15
Introduction
Tissue characterization by ultrasonic measurements may offer a valuable noninvasive
diagnostic tool. Numerous studies have investigated the typical acoustic properties of
normal and abnormal tissues. While most studies of soft tissue properties have focused on
dominant properties such as speed of sound (e.g., Manoharan (1988)) and attenuation (e.g.,
Bhatia and Singh (2001)), less attention has been given to dispersion. Presumably, this
stems from the fact that the speed of sound dispersion phenomenon is very weak and could
be considered to be negligible in most applications.
Measurement of speed of sound dispersion in nonbiological substances was done by
several researchers. Wolfgang and Yih-Hsing (1978) measured the dispersion in dispersive
solids. Chin et al. (1990) and He (1999) measured the dispersion in highly-attenuating
specimens in order to verify the Kramers-Kronig relationship for acoustic waves. Lang et
al. (2000) measured the dispersion in nanocrystalline materials.
Few investigators have studied the speed of sound dispersion in biological tissues.
Kremka et al. (1981) measured the speed of sound dispersion in normal brain. Wear (2000),
Strelitzki and Evans (1996) and Droin et al (1998) measured the dispersion in bones.
Pedersen and Ozcan (1986) measured the dispersion in lung tissues. Carstensen and
Schwan (1959) had measured acoustic properties of hemoglobin solutions.
In most of the above-mentioned studies, the dispersion was calculated by investigating the
variation of the phase as a function of the acoustic wave frequency. Usually, a short
broadband ultrasonic pulse was sent through the object and the phase of each frequency was
extracted using FFT. One limitation of this technique is its relatively low SNR as compared
with continuous wave (CW) measurements. This may induce inaccuracies in phase

16
measurements for each individual frequency. Another challenge in calculation of the
dispersion from a broadband pulse is the determination of the pulse's time of arrival (Zhao
2005). This is a problematic task, since the pulse shape is distorted in dispersive and
attenuating media. This problem was investigated thoroughly by Wear (2001). He (1999)
handled this issue by implementing a trial and error procedure for preparation of the
recorded signal prior to the spectral analysis. Others have used phase unwrapping
procedures (Strelitzki and Evans (1996), Droin (1998), Wear (2000)).
Measurements of speed of sound dispersion using continuous waves were done by Ting
and Sachse (1978) and Pedersen and Ozcan (1986). With their implemented techniques,
many sequential transmissions of continuous waves with increasing frequencies are
required. The technique implemented by Ting and Sachse (1978) requires repeated
measurements of several frequency transmissions through specimens with variable
thicknesses. Pedersen and Ozcan (1986) measured the phase of consecutive frequencies
from nearly-DC to the maximal studied frequency (800 kHz), in order to obtain the
cumulative phase. Both techniques are time consuming.
In the present study, we introduce a method which utilizes a long pulse comprising of two
frequencies, one being the double that of the other. Using this method, we were able to
measure the weak phenomenon of the speed of sound dispersion in soft tissue specimens.
Methods and Materials
Theory
Consider a specimen of an examined material placed between two transducers and
immersed in the water bath (Fig. 1). An ultrasonic harmonic wave with a specific frequency
f is transmitted and travels from point A to point B. The phase of the signal at point A is

17
  0, 2fA f t ft    (1)
where  0 , 0f A f t   is the initial phase of the transmitted wave.
The phase of the wave reaching point B is
     0, , ( ) 2 ( )fB Af t f t t f f t t f        (2)
where ( )t f is the traveling time for an ultrasonic wave of specific frequency f to travel
from point A to point B.
If the distance between points A and B is L and  fc l is the frequency-medium-
dependent phase velocity of the ultrasonic signal along the way from A to B , ( )t f can be
expressed by
 0
1
( )
L
f
t f dl
c l
   . (3)
In a simple configuration, where the medium comprises only water and the examined
specimen, the above integral can be replaced by
,
( ) s s
f s w
L L L
t f
c c

   (4)
where sL is the depth of the specimen, wC is the sound velocity in water (water is
considered as nondispersive medium Carstensen (1954)) and ,f sc is the frequency-
dependent sound velocity of the specimen.
Replacing ( )t f in Eqn 2 yields

18
  0
,
, 2f
s s
B
f s w
L L L
f t f t
c c
  
  
        
  
. (5)
In order to compare the phases of two frequencies, it is convenient to normalize the phase
by2 f , converting it into a time scale,
  0
,
,
2 2
fB s s
f s w
f t L L L
t
f f c c

 
  
       
  
. (6)
If the specimen is dispersive, this term will vary with the frequency. The difference
between the normalized phases of two frequencies 1f and 2f will thus equal
    1 2
1 2
0 01 2
1 2 , , 1 2
, ,
2 2 2 2
f fB B s s
f s f s
f t f t L L
f f c c f f
  
   
      (7)
and, since 0f
 can be set to be zero either by the system setup or by manipulating the data
in postprocessing, we can neglect the last two terms and obtain
   
2 1
1 2
1 2 , ,
, ,
2 2
B B s s
f s f s
f t f t L L
f f c c
 
 
   . (8)
The term on the right hand side is the difference in the time of flight ( )TOF through the
specimen resulting from the speed of sound dispersion,

19
 
2 1, ,
s s
s
f s f s
L L
TOF L
c c
  . (9)
From this equation the, frequency-dependent speed of sound difference for the two
frequencies for a specific specimen, i.e., 2 1, ,f s f sc c , can be determined by
 
1 2 2 1, , , ,
s
f s f s f s f s
s
TOF L
c c c c
L

  . (10)
The group velocity of the sound in the specimen, ,g sc , is related to the phase velocity by
(Strelitzki and Evans 1996)
,
,
,
,
1
f s
g s
f s
f s
c
c
dcf
c df


. (11)
In low-dispersive media, ,f sdc
df
is small and , ,f s g sc c ; therefore, the approximation
2 1
2
, , ,f s f s g sc c c is valid and we get the final form of the variation in the speed of sound,
 
1 2
2
, , ,
s
f s f s g s
s
TOF L
c c c
L

  . (12)
Naturally, there is a linear relation between  sTOF L and the specimen depth sL . Thus,
in order to overcome noise and measurement errors, the variation in the speed of sound can
be calculated from the slope of the curve that describes  sTOF L as function of sL This

20
can be done by repeating each experiment with a given frequency pair 1f and 2f several
times using different specimen depths.
The problem stems from the fact that the phases which are used on the left-hand side of
Eqn 8 are cumulative. However, in practice, only the wrapped phase of each frequency,
 ' ,B f t , is measured (e.g., using the Fourier transform of the recorded signal). Thus, the
left-hand side of Eqn 8 needs to be rewritten as
       1 2 1 1 2 2
1 2 1 2
, , ' , 2 ' , 2
2 2 2 2
B B B Bf t f t f t n f t n
f f f f
     
   
 
   (13)
where 1n and 2n are unknown integers.
In order to overcome this problem, let us consider a special case where the second
frequency equals twice the first frequency, i.e., 2 12f f . In this case, the difference in the
time of flight can be calculated from the wrapped phases,
       1 1 1 2 1 1 1 2
1 1 1 1 1
' , 2 ' 2 , 2 ' , ' 2 , 2
2 4 2 4 2
B B B Bf t n f t n f t f t n n
f f f f f
     
   
  
    . (14)
Thus, in this configuration, the cumulative phases are not needed any more for
calculating  sTOF L : we just have to find the integer 1 22m n n  . After rearrangement
and substituting into Eqn 8, we obtain,

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 
   1 1
1
' , ' 2 ,
2
2
B B
s
f t f t
m f TOF L
 
 
    . (15)
If the dispersion is very low (as is the case in many materials), then  sTOF L is very
small as well. In the case that the nondimensional parameter fulfils the condition
 12 0.5sf TOF L  , the integer m can be simply found by
   1 1' , ' 2 ,
2
B Bf t f t
m round
 
 
 
   
 
(16)
where round[] is the operation of rounding to the nearest integer. Therefore,  sTOF L
can be determined from
 
   
       
1 1
1 1 1
1 1 1 1
1 1 1
' , ' 2 ,
2 4 2
' , ' 2 , ' , ' 2 ,1
.
2 4 2 2
B B
s
B B B B
f t f t m
TOF L
f f f
f t f t f t f t
round
f f f
 
 
   
   
    
 
      
 
(17)
By substituting this equation into Eqn 10, the value of ( 2 1, ,f s f sc c ) can be determined.
Finally, by using this value, a dispersion index is defined as
2 1
1 2
2 1
( , )
f fc cc
f f
f f f

  
 
. (18)
Ultrasonic Measurements
The scanning system utilized to measure the plastic specimens is comprised of a water-bath
with a specially-built computer-controlled mechanism that can produce spatial motion with

22
three degrees of freedom for a pair of transducers (Panametrics, 5 MHz, focused
transducers, diameter 12.7 mm and focal length 10.7cm) placed about twice the focal length
apart (Azhari and Stolarski (1997), Azhari and sazbon (1999)). The system can scan a
cylindrical volume defined by the user (up to 20 cm in diameter and 10 cm in height)
located at the center of the water bath.
Signals were generated by a Tabor 8026 arbitrary wave-form generator and a Panametrics
5800 pulser/receiver was used as a receiver. A Gage CompuScope 12100 two-channel 50-
MHz 12-bit A/D converter was used digitally to store the detected waves.
The experimental procedure for the plastic specimens started by acquiring an ultrasonic
projection depicting the TOF of the step phantom, using a short ultrasonic pulse. This
projection was used for calculating the group velocity ,g sc of the sound in the specimen.
Afterwards, a continuous wave, which was built by mixing a pair of sinusoidal waves with
frequencies f and 2f, was generated. The initial phase for both frequencies was set to zero
using the signal generator. The two steps can be combined into a single measurement, as
shown in Fig 2. The transmitted continuous wave was actually a long but finite sinusoidal
train with a defined front. A rect sampling window was taken from the front end of this
train and its length was set to be shorter than the time needed for the first reverberation to
occur. This was done in order to avoid measurement artifacts stemming from the formation
of standing waves in the specimens. At least 12 µs of the wave were sampled by the A/D
for signal analysis.
Using Eqn 17, the corresponding TOF was calculated for each step in the phantom. A
plot depicting  sTOF L as a function of sL was then obtained by combining all the
results. Using the least-squares method, a straight line was fit to this set of data. Then the
velocity difference between ,s fc and ,2s fc was found from the slope of the fitted line. It

23
should be clarified that the line-fitting stage is not a necessity for the suggested method, but
was implemented in order to augment the accuracy of our calculation. (The values could be
readily extracted from a single measurement, as explained in the previous section, eqn 12.)
The above procedure was repeated several times using waves composed of different pairs
of frequency mixtures ranging from {1 MHz and 2 MHz} to {3 MHz and 6 MHz}. Finally,
combining all the obtained results, the dispersion index 1 2( , )f f defined in Eqn 18 was
plotted versus the average frequency used, i.e., 2 1( )/ 2f f .
A slightly different set-up was implemented for the soft tissue specimens. Instead of
scanning different tissue samples with various thicknesses, the same sample was placed
within a plastic cylinder (10 cm in length and 4 cm in diameter) positioned between the
transducers pair so that its axis was aligned with the line of sight connecting the two
transducers. After completing one set of measurements, as described above, the tissue
sample was slightly pushed out of the cylinder and a small slice was cut and removed
(similar to cutting a salami, see also scissors icon in Fig.1). Then, the above procedure was
repeated and a new set of measurements was obtained. This was done to ensure that the
only parameter changed between measurements was the tissue thickness, assuming that the
acoustic properties were constant throughout the sample.
In addition, to ensure that the plastic cylinder did not affect the measurements, a
comparative study was done in water, with and without the cylinder. The signals were
compared and no changes were observed.
All the above experiments were done at room temperature (about 21o
C).

24
Specimens
In this research, the dispersion was first studied in two plastic materials and then in two
soft tissues (in-vitro). The plastics were polyvinylchloride (PVC) and
polymethylmethacrylate (perspex). They were studied in order to validate the method, to
establish some standard reference and to allow comparison with results published by others.
The soft tissues used here were bovine heart and turkey breast. The soft tissue specimens
had been refrigerated until the experiment.
In order to increase the accuracy and reliability, several measurements of each specimen
with varying thicknesses were done. Several thicknesses of the plastic specimens were
obtained by building a “step-phantom” with parallel faces, varying in distances from 2 cm
to 3 cm from each other. Small slices were chopped from the soft tissue specimens during
the experiment, in order to measure several widths of each soft tissue specimen. The
thicknesses of the plastic specimens were measured with a caliper (accuracy ±0.1 mm). The
thicknesses of the tissue specimens were calculated using two steps. First, the speed of
sound in the tissue was estimated. Then, by the measuring the TOF, the thickness was
determined (estimated accuracy ±1 mm).
Results
Plastic Specimens
The calculated dispersion index 1 2( , )f f versus 2 1( )/ 2f f obtained for the PVC
specimen is plotted in Fig 3. The average values for each pair of frequencies studied are

25
depicted along with their corresponding 95% confidence level range (vertical bars). As can
be noted, the dispersion index is positive throughout the studied range of frequencies but
monotonically decreases from 9.7 ± 2.5 (m/sMHz) at 1.5 MHz to 2.9 ± 0.5 (m/sMHz) at
4.5 MHz. Also, as can be noted, the relative scatter of the data tends to decrease as the
frequency is increased.
The dispersion index 1 2( , )f f versus 2 1( )/ 2f f for the perspex specimen is presented
in Fig 4. As can be observed, the dispersion index values are smaller compared with those
obtained for the PVC. Also, one may note again that the dispersion index is higher for the
lower frequency range and that it decreases as the frequency increases. The abrupt increase
in 1 2( , )f f from 1.5 MHz to 1.875 MHz may be attributed to measurement errors (note
the large 95% confidence range). The dispersion index decreases in this case from 6.5 ± 4
(m/sMHz) at 1.5 MHz to 1.5 ± 0.5 (m/sMHz) at 4.5 MHz.
Soft Tissues
A demonstrative data set obtained for the turkey breast specimen, depicting  sTOF L
as a function of sL for the frequency pair {2.25 MHz and 4.5 MHz}, is shown in Fig. 5.
The linear relation is clearly noted. The negative  sTOF L values stem from the fact that
the speed of sound increases with the frequency for the range studied here. As can be noted,
 sTOF L in this case ranges from about 10 ns to 60 ns. The speed of sound dispersion
index for the turkey breast is presented in Fig. 6. Again, the trend for a decrease in
1 2( , )f f as the frequency increases is noted. The dispersion index decreases in this case
from 1.3 ± 0.28 (m/sMHz) at 1.75 MHz to 0.73 ± 0.1 (m/sMHz) at 3.8 MHz. These values
are significantly smaller than those obtained for the plastic specimens.

26
The speed of sound dispersion index values obtained for the bovine heart are presented in
Fig. 7. As can be noted, in this case, the dispersion indices are generally smaller than those
obtained for the turkey breast. The tendency for the dispersion index to decrease with the
frequency can be noted. However, although the dispersion index values in the frequency
range studied were reduced by 50%, the rate of decrease is more moderate than for the
turkey breast. The dispersion index decreases, in this case, from 0.63 ± 0.24 (m/sMHz) at
1.5 MHz to 0.27 ± 0.05 (m/sMHz) at 4.5 MHz.
Discussion
A novel method for measuring the speed of sound dispersion has been introduced and its
application in soft tissue specimens has bean demonstrated. It combines a short (broad-
band) pulse transmission followed by a long burst comprising of two frequencies, one being
double the other. The method allows the determination of the dispersion using a single
transmission. Although we have used here data obtained from several tissue thicknesses, it
should be pointed out that this is not a necessity for the suggested method, but was done in
order to improve the accuracy of our calculations. Also, the method does not require
absolute phase evaluation or any phase unwrapping procedure.
Studying our findings in the plastic specimens reveals that our dispersion measurements
in perspex are in excellent agreement with He's (1999) results. We have measured 7 ± 4
(m/sMHz) at 1.5 MHz and 2 ± 0.4 (m/sMHz) at 3.8 MHz. According to He’s (1999)
measurements (which were obtained using a short pulse method), the speed of sound
dispersion at 1.25 MHz is around 7 (m/sMHz) and it is around 2.5 (m/sMHz) at 3.5 MHz.
This provides a validation to the reliability of our suggested method.

27
Carstensen and Schwan (1959, Fig 6) had measured acoustic properties of hemoglobin
solutions and found that the speed of sound dispersion in beef hemoglobin
(30 g Hb/100 ml , 250
C) at 1 MHz is around 0.7 (m/sMHz) and it is around 0.25
(m/sMHz) at 4 MHz. Kremkau et al. (1981) measured the speed of sound dispersion in
normal brain to be 1.2 (m/sMHz) and 1 (m/sMHz) for fresh and fixed tissue, respectively.
Our results are in the same order of magnitude.
Positive dispersion (i.e., the speed of sound increases with the frequency) was found for
all the studied specimens. The dispersion index, on the other hand, decreases as a function
of the frequency in all the studied materials. This behavior agrees with the results reported
by Chin et al. (1990) for polyurethane and He (1999) for perspex and Carstensen and
Schwan (1959, Fig 6) for hemoglobin solutions. Droin et al. (1998) and Wear (2000)
reported similar trends for polycarbonate specimens.
Naturally, the structure of bones differs substantially from that of soft tissues.
Nevertheless, it is worth noting that, comparing the results obtained for the soft tissue
specimens in this study with those reported for bones, reveals opposite trends. In bones,
negative dispersion was reported by Wear (2000), Strelitzki and Evans (1996) and Droin et
al (1998).
Another observation obtained in this study is the consistent decrease in the dispersion
index scatter with the increase in frequency. This is indicated by the smaller size of the 95%
confidence range in Figs. 3,4,6 and 7 for the higher frequencies. This may be attributed to
the lower ultrasonic diffraction occurring at high frequencies. Due to the diffraction
phenomenon, which is more dominant for the lower frequency waves, the acoustic paths

28
may be slightly different for different frequency waves and that may consequently change
the TOF .
In conclusion, a novel method for measuring the speed of sound dispersion has been
introduced. With this method, dispersion in soft tissues was measured. The differences in
the dispersion index between the studied materials were found to be significant. This
indicates that dispersion may be used as a new index for soft tissue characterization by
ultrasound if a through transmission imaging technique (e.g., ultrasonic breast CT) is
utilized to map its variations in a studied object.

29
Acknowledgments
The authors are grateful for funding provided by the Galil Center For Telemedicine And
Medical Informatics and by the Technion V.P.R. Research funds, Eliyahu Pen Research
fund, Dent Charitable Trust, Japan Technion Society and the Montréal Biomedical Fund.
Finally we thank Mr. Aharon Alfasi for his extremely valuable technical support.

30
References
Azhari H, Stolarski S. Hybrid ultrasonic computed tomography. Comput Biomed Res. 1997
Feb;30(1):35-48.
Azhari H, Sazbon D. Volumetric imaging with ultrasonic spiral CT. Radiology
1999;212(1):270-275.
Bhatia KG, Singh VR. Ultrasonic characteristics of leiomyoma uteri in vitro. Ultrasound
Med Biol. 2001;27:983-987.
Carstensen EL. Measurement of Dispersion of Velocity of Sound in Liquids. J. Accoust.
Soc. Am 1954;26:858-861.
Carstensen EL, Schwan HP. Acoustic Properties of Hemoglobin Solutions. J Accoust Soc
Am 1959;31:305-311
Chin C, Lahham M, Martin BG. Experimental Verification of the Kramers-Kronig
Relationship for Acoustic Waves IEEE Trans Ultrason Ferroelectr Freq Control
1990;37:286-294.
Droin P, Berger G, Laugier P. Velocity Dispersion of Acoustic Waves in Cancellous Bone.
IEEE Trans Ultrason Ferroelectr Freq Control 1998;45:581-592.
He P. Experimental Verification of Models for Determining Dispersion from Attenuation.
Kremkau FW, Barnes RW, McGraw CP. Ultrasonic attenuation and propagation speed in
normal human brain. J Accoust Soc Am 1981;70:29-38.
Lang MJ, Duarte-Dominguez M, Arnold W. Extension of frequency spectrum methods for
phase velocity measurements in ultrasonic resting. Rev Sci Instrum 2000;71:3470-3473.

31
Manoharan A, Chen CF, Wilson LS, Griffiths KA, Robinson DE. Ultrasonic
characterization of splenic tissue in myelofibrosis: further evidence for reversal of fibrosis
with chemotherapy. European-journal-of-haematology 1988;40:149-154.
Pedersen PC, Ozcan HS. Ultrasound properties of lung tissue and their measurements.
Ultrasound Med Biol. 1986 Jun;12(6):483-99.
Wolfgang S, Yih-Hsing P. On the determination of phase and group velocities of dispersive
waves in solids J. Appl. Phys. 1978;49(8):4320-4327.
Strelitzki R, Evans JA. On the measurements of the velocity of ultrasound on the os calcis
using short pulse. European Journal of Ultrasound 1996;4:205-213.
Ting CS. Sachse W. Measurement of ultrasonic dispersion by phase comparison of
continuous harmonic wave. J Acoust Soc Am 1978;64(3):852-857.
Wear KA. Measurments of phase velocity and group velocity in human calcaneus.
Ultrasound Med Biol 2000;26:641-646.
Wear KA. A numeric method to predict the effect of frequency-dependent attenuation and
dispersion on speed of sound estimates in cavcellous bone. J Acoust Soc Am
2001;109(3):1213-1218.
Zhaoa B, Basira OA, Mittal GS, Estimation of ultrasound attenuation and dispersion using
short time Fourier transform, Ultrasonics 2005;43(5);375-381.

32
List of Figures captions.
Fig. 1. A Schematic depiction of the experimental system used here. A specimen of an
examined material was placed in water between two transducers. An ultrasonic wave was
transmitted through the specimen from A to B, detected and digitized. The specimen was
sliced (symbolized by the scissors icon) between different measurements to vary its
thickness (see text).
Fig. 2. Schematic depiction of the transmitted waves needed for the suggested method. A
short pulse transmission which is used for measuring the group velocity Cg is followed by a
long burst comprising of two frequencies, one being the double of the other.
Fig. 3. The speed of sound dispersion index 1 2( , )f f versus 2 1( )/ 2f f for the PVC
specimen. The error bars correspond to the 95% confidence level range.
Fig. 4. The speed of sound dispersion index 1 2( , )f f versus 2 1( )/ 2f f for the perspex
specimen. The error bars correspond to the 95% confidence level range.
Fig. 5. A demonstrative data set obtained for the turkey breast specimen, depicting
 sTOF L as a function of sL for the frequency pair {2.25 MHz and 4.5 MHz}.
Fig. 6. The speed of sound dispersion index 1 2( , )f f versus 2 1( )/ 2f f for the turkey
breast. The error bars correspond to the 95% confidence level range.
Fig. 7. The speed of sound dispersion index 1 2( , )f f versus 2 1( )/ 2f f for the bovine
heart. The error bars correspond to the 95% confidence level range.

40
Paper B: "Ultrasonic Speed of Sound Dispersion Imaging"
Abstract
The feasibility for speed of sound dispersion (SOSD) imaging was investigated here. A
through transmission new method for measuring the SOSD was utilized. With this method
a long pulse comprising of two frequencies one being the double of the other is transmitted
through the object and detected on its other side. SOSD projection images were obtained by
scanning objects immersed in water using a raster mode utilizing a computerized scanning
system. Using this approach SOSD projection images were obtained for solids and fluids as
well as for a tissue mimicking breast phantom and an in-vitro soft tissues phantom. The
results obtained here, have clearly demonstrated the feasibility of SOSD projection
imaging. SOSD may serve as a new contrast source and potentially may aid in breast
diagnosis.
Keywords: Medical imaging, Ultrasound, Speed of sound Dispersion, Tissue
characterization.

41
Introduction
The speed of sound dispersion (SOSD) phenomenon in soft tissues is very weak (Wells
1999), therefore, it is difficult to detect and measure and hence it was neglected in most
applications. However, several techniques for SOSD measurements have been suggested
and implemented for in-vitro specimens. For example, SOSD was measured in human
brains by Kremkau et al. (1981), in lungs by Pedersen and Ozcan (1986), in hemoglobin
solutions by Carstensen and Schwan (1959). Also, Marutyam et al. (2006) have measured
SOSD in lamb hearts, and Akashi et al. 1997 and Levy et al. (2006) in bovine hearts.
Recent studies indicated that speed of sound dispersion (SOSD) may be used for
ultrasonic tissue characterization. Marutyam et al. (2006) reported that the SOSD depends
on the orientation of anisotropic tissue. Levy et al. (2006) have shown that there is a
significant difference in the dispersion index between different specimens.
In Levy et al. (2006) a method for measuring the speed of sound dispersion using a single
transmission which utilizes a long pulse comprising of two frequencies, one being the
double that of the other was introduced. This method is suitable for imaging using a through
transmission mode. The objective of this study was to investigate the feasibility of utilizing
this method for SOSD imaging.
Theory
Consider an examined object (e.g. woman breast) placed between two transducers and
immersed in the water bath (Fig. 1). An ultrasonic signal which is comprised of two

42
frequencies f1, f2 is transmitted and travels from point A to point B. Using spectral analysis,
the signal can be decomposed into its two disjoint components. The phase of each
component at point A is
  0, 2fA f t ft    (1)
where  0 , 0f A f t   is the initial phase of the transmitted wave.
The phase of the wave reaching point B is
     0, , ( ) 2 ( )fB Af t f t t f f t t f        (2)
where ( )t f is the traveling time for an ultrasonic wave of a specific frequency f to
travel from point A to point B.
If the distance between points A and B is L and  fc l is the frequency-medium-
dependent phase velocity of the ultrasonic signal along the way from A to B , ( )t f can be
expressed by
 0
1
( )
L
f
t f dl
c l
   (3)
In order to compare the phases of two frequencies, it is convenient to normalize the phase
by2 f , converting it into a time scale,
 
 
0
0
, 1
2 2
f
L
B
f
f t
t dl
f f c l

 
 
     
 
 . (4)

43
The difference between the normalized phases of two frequencies 1f and 2f will thus be
equal to
   
   
1 2
2 1
0 01 2
1 2 1 20
, , 1 1
2 2 2 2
f f
L
B B
f f
f t f t
dl
f f c l c l f f
  
   
 
      
  
 (5)
and, since 0f
 can be set to equal zero either by the system's hardware setup or by post
processing, we can neglect the last two terms and obtain
   
   2 1
1 2
1 2 0
, , 1 1
2 2
L
B B
f f
f t f t
dl
f f c l c l
 
 
 
    
  
 . (6)
The term on the right hand side is the difference in the time of flight from point A to point
B through the imaged object between frequency f1 and frequency f2 resulting from the speed
of sound dispersion. This time of flight difference is denoted by 1 2TOF f f ( , ) . Water is
considered as nondispersive medium (Carstensen 1954), therefore, the frequency-
dependence of the time of flight represents solely the imaged object properties. Defining
1 2TOF f f ( , ) per unit length  at distance l from the transmitter as
   2 1
1 2
1 1
( , , )
f f
l f f
c l c l
  (7)

44
the time difference between the normalized phases of two frequencies 1f and 2f can be
written as
   1 2
1 2 1 2
1 2 0
, ,
( , ) ( , , )
2 2
L
B Bf t f t
TOF f f l f f dl
f f
 
 
      . (8)
Hence, measurement of the difference between the normalized phases gives a projection of
the accumulative  along the track from A to B. Nevertheless, it is not trivial to obtain this
measurement since the phases which are used on the left-hand side of Eqn (8) are
cumulative and can exceed 2 . Thus, in practice, only the wrapped phase of each
frequency,  ' ,B f t , is measured (e.g. using the Fourier transform of the recorded signal).
In order to overcome this problem, let us consider a special case where the second
frequency equals twice the first frequency, i.e., 2 12f f . In case that the nondimensional
parameter fulfils the condition 1 1 1
0
2 ( , ,2 ) 0.5
L
f l f f dl   , it was shown by Levy et al.
(2006) that the difference in the time of flight can be calculated from the wrapped phases
       1 1 1 1
1 1
1 1 10
' , ' 2 , ' , ' 2 ,1
( , ,2 )
2 4 2 2
L
B B B Bf t f t f t f t
l f f dl round
f f f
   
   
 
        
 
 (9)
where round[] is the operation of rounding to the nearest integer.
In order to reconstruct a projection image 1I x y f( , , ) of the SOSD, the object can be
scanned in a raster mode, so as to depict the relation

45
1 1 1
0
( , , ) ( , , , ,2 )
L
I x y f x y z f f dz   . (10)
The constraint 1 1 1
0
2 ( , ,2 ) 0.5
L
f l f f dl   is mandatory for accurate measurement of the
accumulative dispersion. However, for imaging proposes it is sufficient to avoid phase
wrapping in the region of interest (ROI). Therefore, the constraint is on the variation of the
accumulative dispersion in the ROI
1 1 1 1
10 0
1
max ( , , , ,2 ) min ( , , , ,2 )
2
L L
ROI x y l f f dl x y l f f dl
f
   
          
   
  (11)
where { , }x y ROI .
Ultrasonic Measurements
The scanning system utilized to generate the accumulative dispersion index projection of
the imaged object comprised of a water tank with a specially built computer controlled
mechanism that can produce spatial motion with three degrees of freedom for a pair of
transducers (Panametrics, 5 MHz, focused transducers, diameter 12.7 mm and focal length
10.7cm) placed about twice the focal length apart (Azhari and Stolarski (1997), Azhari and
sazbon (1999)). The system can scan a cylindrical volume defined by the user (up to 20cm
in diameter and 15cm in height) located at the center of the water tank. In the imaging
configuration utilized here the object was scanned in a raster mode, yielding a rectangular
projection image 1I x y f( , , ) (see eqn.(10)). The scanning resolution was set by the user
before each scan. Typical scanning resolution was 0.3mm X 1mm along the horizontal and
vertical directions respectively.

46
5800 pulser/receiver was used as a receiver. A Gage CompuScope 12100 two-channel 50-
MHz 12-bit A/D converter was used digitally to store the detected waves.
The experimental procedure
A continuous wave, which was constructed by mixing a pair of sinusoidal waves with
frequencies f and 2f, was generated. The initial phase for both frequencies was set to zero
using the signal generator control. The transmitted continuous wave was actually a long but
finite sinusoidal train. A long rect sampling window from the received signal was used for
the spectral analysis. At least 12 µs of the wave were sampled by the A/D for signal
analysis.
Using Eqn (9), the corresponding time of flight difference was calculated for each
measurement point. An image depicting a projection of the accumulative dispersion index
1I x y f( , , ) was then obtained.
All experiments were done at room temperature (about 21o
C).
Imaged Objects
The accumulative dispersion index projections 1I x y f( , , ) were acquired for four objects:
(i) a plastic step phantom, (ii) a commercial breast phantom, (iii) a balloon with three
different fluids and (iv) a biological phantom comprised of two soft tissues (in-vitro).

47
The step phantom (see Fig.2 top) was made of polyvinylchloride (PVC). The step size was
2 mm and the minimal thickness was 2 cm. The breast phantom was an ATS Laboratories
Model BB-1 breast phantom. The BB-1 mimics the geometry and acoustic properties of the
human breast and contains target structures randomly embedded within a tissue mimicking
material. The balloon was filled with soybean oil, water and glycerin (Purity min 98%, by
Frutarom LTD.). Due to the differences in densities, the soybean oil floated on top of the
water and the glycerin sank below the water. The two in-vitro soft tissue specimens used
here were bovine heart and turkey breast (specimens were obtained from a local
commercial slaughterhouse). The soft tissue specimens were stored in a refrigerator (they
were not frozen) and were brought to room temperature before the experiment. To eliminate
the influence of thickness on the results the specimens were cut to have the same thickness
(3 cm).
Results
The projection of the accumulative dispersion index 1I x y f( , , ) , obtained for the PVC
step phantom (f1 = 2.5 MHz) is shown in Fig 2 (bottom). As can be noted the individual
steps are clearly visible, reflecting the increased time of flight difference, 1 2TOF f f ( , ) ,
resulting from the increased thickness. Darker colors represent higher accumulative
dispersion index values. The accumulative SOSD mean difference between each step and
the thinnest step were: 0.7, 1.9, 3.6, 4.4, 6.0 [nanosecond] (see Fig 3). Applying linear
regression to the data, the typical value of  for PVC was found from the slope of the
regression line and its value was 6.51.1 [nanoseconds/cm] (with 95% confidence level).

48
The projection of the accumulative dispersion index 1 1 5I x y f MHz( , , . ) obtained for the
three fluids phantom is depicted in Fig 4. As can be noted, there is a clear contrast between
the regions containing the different fluids. Darker color indicates higher SOSD. The
intermediate layer between the Glycerin and the water stems from a mixture of fluid
bubbles formed when the water was poured atop the Glycerin.
The projection of the accumulative dispersion index 1= 1 MHzI x y f( , , ) obtained for the
BB1 commercial breast phantom is depicted in Fig 5. In this case, lower frequencies were
used in order to improve the penetration trough the phantom. As can be observed the
embedded targets (some of which are marked by arrows) depict high accumulative
dispersion index values. Importantly it should be clarified that although dispersion in water
is negligible, in this image it appears as a dark region. This stems from the fact that the
condition of 1 1 1
0
2 ( , ,2 ) 0.5
L
f l f f dl   (see above) was not met for the water and hence in
this case a 2 phase wrapping occurred. However, the region of interest, i.e. the breast
phantom, has complied with condition (11).
The projection image of the accumulative dispersion index obtained for the in-vitro soft
tissue phantom (f1 = 2.5 MHz) is depicted in Fig 6. As can be noted, there is a significant
difference in gray levels between the regions containing the two types of tissues. Both
tissue specimens had the same thickness. Thus, the only source of contrast is the SOSD. As
can be noted the SOSD is higher for the turkey breast tissue.
Discussion
SOSD has been suggested as an additional acoustic property for utilization in medical
applications. The most discussed idea was to use SOSD for bone assessment (Wear (2000),

49
Strelitzki and Evans (1996), Droin et al (1998)). Analysis of SOSD in soft tissues has also
been conducted, (e.g. in brain by Kremkau et al. (1981), in lung by Pedersen and Ozcan
(1986), in hemoglobin solutions by Carstensen and Schwan (1959), and in hearts by Akashi
et al. 1997 and by Marutyam et al. (2006)). To the best of our knowledge SOSD imaging
has not been suggested. This may stem from two main reasons. First SOSD is a very weak
phenomenon and hence difficult to measure. And secondly previously suggested methods
had either low SNR or required too long acquisition times.
The method suggested by Levy et al. (2006), offers improved SNR and a single
transmission measurement of the SOSD. This makes it particularly suitable for ultrasonic
SOSD projection imaging as was demonstrated by the results.
There are two challenges associated with the suggested method: (a) boundary artifacts and
(b) phase wrapping. As can be noted (Figs.2,4,5,6), there is an artifact which occurs at
boundaries separating different regions in the imaged object. This artifact appears as a
strong gradient in SOSD values. It emphasizes boundaries and hence, may increase the
visibility of small targets. The source of this artifact may be the frequency-dependent
acoustic diffraction which occurs at such boundaries.
As for phase wrapping, the constraint on the variation of the accumulative dispersion in
the ROI (Eq.(11)), imposes a limit on the allowed variation of the SOSD property in the
imaged object. Violation of this constraint may lead to a phase wrapping in certain regions
within the image. (A problem which resembles the phase wrapping problem of MRI Phase
contrast flow imaging). Algorithms for phase unwrapping may be needed in such cases.
In conclusion, the results obtained here, have clearly demonstrated the feasibility of
SOSD projection imaging. As was shown here, SOSD images can be obtained for solids
(Fig.2), for fluids (Fig.4) as well as for the tissue mimicking breast phantom (Fig.5) and soft

50
tissues (Fig.6). SOSD may serve as a new contrast source and potentially may aid in breast
diagnosis.
Acknowledgments
The authors are grateful for funding provided by the Technion V.P.R. Research funds,
Eliyahu Pen Research fund, Dent Charitable Trust, Japan Technion Society and the
Montréal Biomedical Fund. Finally we thank Mr. Aharon Alfasi for his extremely valuable
technical support.

51
References
Akashi N, Kushibiki J, Chubachi N, Dunn F. Acoustic properties of selected bovine tissues
in the frequency range 20–200 MHz. J Acoust Soc Am 1995;98:3035–3039.
Feb;30(1):35-48.
1999;212(1):270-275.
Carstensen EL, Schwan HP. Acoustic Properties of Hemoglobin Solutions. J Accoust Soc
Am 1959;31:305-311
Kremkau FW, Barnes RW, McGraw CP. Ultrasonic attenuation and propagation speed in
normal human brain. J Accoust Soc Am 1981;70:29-38.
Levy Y, Agnon Y and Azhari H. Measurement of Speed of Sound Dispersion in Soft
Tissues Using a Double Frequency Continuous Wave Method UMB 2006;32(7):1065-
1071.
Marutyan RK, Yang M, Baldwin SL, Wallace KD, Holland MR, And Miller JG. The
Frequency Dependence of Ultrasonic Velocity And The Anisotropy Of Dispersion In Both
Freshly Excised And Formalin-Fixed Myocardium. Ultrasound Med Biol. 2006; 32(4):603–
610.
Pedersen PC, Ozcan HS. Ultrasound properties of lung tissue and their measurements.
Ultrasound Med Biol. 1986 Jun;12(6):483-99.

52
Wells P N T, Ultrasonic imaging of the human body, Rep. Prog. Phys. 1999;62:671-722.
Zhaoa B, Basira OA, Mittal GS, Estimation of ultrasound attenuation and dispersion using
short time Fourier transform, Ultrasonics 2005;43(5);375-381.

53
Figure captions.
Figure 1: Schematic depiction of the system's measurement setup. An object is placed in a
water tank between two ultrasonic transducers. A signal is transmitted from one transducer
and detected after passing through the object by the other transducer. An image is obtained
by scanning the object along a set of horizontal lines (raster mode).
Figure 2: (Top) a Photo of the PVC step phantom. (Bottom) its corresponding SOSD
projection image. The thickness of the steps is incrementally increased by 2 mm starting
from 20 mm.
Figure 3: The measured increase in the accumulative SOSD (marked by *) relative to the
thinnest step obtained for each step of the PVC phantom as a function of the increase in the
step's thickness. The solid line corresponds to the calculated regression line.
Figure 4: A SOSD projection image of the phantom containing three fluids. Note the
contrast between the layers. (The intermediate layer between the Glycerin and the water
stems from a mixture of fluid bubbles formed when the water was poured atop the
Glycerin).
Figure 5: A SOSD projection image obtained for the commercial breast phantom. The
embedded targets have formed regions of discontinuity within the phantom matrix
(indicated by the arrows).

54
Figure 6: A SOSD projection image obtained for the in-vitro tissue phantom. Both tissue
specimens had the same thickness. Thus, the only source of contrast is the SOSD. As can be
noted the SOSD is higher for the turkey breast tissue.

55
Fig. 1
B
Signal Generator Amplifier / Filter
A/D
Trigger
Transmitter
Imaged
Object
A
Receiver

56
Fig 2.
Photo of the Steps Phantom
SOSD Projection image
Photo of the Steps Phantom
SOSD Projection image

58
Fig. 4.
Soybean
oil
Water
Glycerin
Soybean
oil
Water
Glycerin

60
Fig. 6.
Bovine
heart
Turkey
breast

61
Paper C: "Speed of Sound Dispersion Measurement Using a Chirp Signal"
SPEED OF SOUND DISPERSION
MEASUREMENT USING A CHIRP SIGNAL
Yoav Levy1
, Yehuda Agnon2
and Haim Azhari1
1
Faculty of Biomedical Engineering
And
2
Faculty of Civil and Environmental Engineering
Technion, IIT, Haifa, Israel, 32000

62
Abstract
In this study, two new methods for speed of sound dispersion measurement were
developed. These methods are based on transmission of a linear frequency modulated
“chirp” pulse. The first method, entitled as the "signals bank method" is based on
assessment of similarity between the measured signal and a synthesized bank of signals.
This method is robust and performs well even at high frequencies where the signal is more
attenuated. However, it requires a relatively long computation time (several seconds on a
PC). The second method, titled the: "cross correlation method" is computationally faster
and is based on calculation of the phase of the peak of the complex cross correlation
function. Therefore it is valid only for narrowband measurements and it may be biased by
frequency dependent attenuation.
To the best of our knowledge, using these methods, speed of sound dispersion was
measured in the pulse-echo mode in soft tissues for the first time. Both methods are suitable
for projection imaging as well.
Keywords: ultrasound, speed of sound dispersion, chirp, pulse-echo, soft tissue.

63
Introduction
Quantitative ultrasound (QUS) is a method for pathologies diagnostic which was suggested
many years ago (Greenleaf 1986). There are several acoustic properties which are used for
tissue characterization such as speed of sound (Manoharan 1988), sound attenuation (Bhatia
and Singh 2001), average ultrasonic scatterer size (Mamou 2006) and other. However, more
contrast sources are needed in order to improve the reliability of the QUS diagnostic results.
Speed of sound dispersion (SOSD) may serve as a new source for ultrasonic contrast.
Methods for measurement of SOSD based on the analysis of broadband pulses were applied
to study solids and bones (He 1999, Strelitzki and Evans 1996, Droin 1998 and Wear
2000). However, SOSD phenomenon is very weak in soft tissues (Wells 1999) and hence is
difficult to measure. Few investigators have studied the speed of sound dispersion in
biological soft specimens. Kremka et al. (1981) measured the speed of sound dispersion in
normal brain, Pedersen and Ozcan (1986) measured the dispersion in lung tissues.
Carstensen and Schwan (1959) had measured acoustic properties of hemoglobin solutions
and Marutyan et al (2006) have studied it in myocardial tissue. All these methods are either
relatively slow or require high SNR. In more recent studies it was shown that the SOSD
may be rapidly measured in soft tissues (Levy et al 2006) and may be used for medical
imaging (Levy et al 2007).
All the above mentioned methods have utilized through transmission waves. However, this
limits their potential application in ultrasonic imaging and tissue characterization. A pulse-
echo based technique is more desirable since it offers much better accessibility to many
organs in the body. In this study two new methods for speed of sound dispersion

64
measurements using a pulse-echo as well as through transmission technique and a chirp
signal are introduced. The methods were tested in both through and pulse-echo modes.
Theory
Consider an examined homogeneous object placed between two transducers and
immersed in the water bath. An ultrasonic linearly modulated signal (chirp) is transmitted
from point A, travels through the object and recorded at point B. Alternatively, a single
transducer is used and the echo reflected from its back face is recorded. The signal is
distorted by a frequency dependent dispersion of the phase velocity in the object. This
phase velocity dispersion depends on the object's material. In this section two alternative
methods for measuring the dispersion of the phase velocity are derived. The first method is
based on finding the maximal similarity of the measured signal and a synthesized signal
taken from a pre-calculated bank of synthetic signals. The second method utilizes an
analysis of the cross correlation function between the measured signal and a reference
signal.
The Synthetic Signals Bank Method
The first method is based on a model which describes the distortion of a signal by a
dispersive medium. Wear (2001) described the distorted signal  y t recorded at point B, by
a convolution of the undistorted reference signal,  x t , and the impulse response of the
object  h t

65
(1)   *yt xt ht
The reference signal is the signal obtained for a wave which travels from point A to Point B
through the water (assumed to be non-dispersive (Carstensen 1954)) or the echo reflected
from a reference surface in the absence of the object. The Fourier transform of  h t may be
modeled by,
(2)   22 fd i f tf
Hf Te e   

where f is the frequency, T is the transmission coefficient at the water-object borders,  is
an attenuation coefficient, d is the thickness of the object and t(f) is the time delay of a
given frequency relative to the reference signal. t(f) is given by (see Wear 2001):
(3) 

1 1
s w
t f d
cf c
 
    
 
where wc is the speed of sound in water and  sc f is the phase velocity in the object. The
time delay t(f) can be divided into two components: (a) 0t and (b)  dt f where
(4)
 0
0s w
d d
t
c f c
  

and
(5)  
   0
d
s s
d d
t f
c f c f
  

.
Where  0sc f  corresponds to a frequency independent component of the phase
velocity. Hence, the term 0t describes the frequency independent time of flight difference

66
between the signal traveling through the object and the reference signal. This term causes a
“pure” time shift of the signal and preserves the signal's shape (i.e. no distortion). The
second term  dt f is a small perturbation of the first term which takes into account the
dispersion of the phase velocity in the medium. This term induces distortion in the signal’s
shape when traveling through the object. Therefore, for modeling the dispersion induced
distortion in the signal’s shape, the “pure” signal’s time shift may be ignored as well as the
intensity scaling caused by the transmission coefficient, 2
T . Consequently, the shape
distortion transfer function  dH f may be modeled by
(6)   2 dfd i f t f
dHf e e   

While  dt f is not known, the attenuation coefficient,  f , can be calculated by
comparing the spectra of the distorted signal to the reference spectrum and the object's
thickness, d, is measurable.
Consider a narrowband linear frequency modulated chirp signal. For this signal the phase
velocity as a function of the frequency may be approximated by a linear function (Wear
2000)
(7)      s s c s cc f c f b f f   
where fc is the center frequency of the transmitted signal and sb is a slope of the phase
velocity function. In the narrow band case, the attenuation coefficient part  f d
e

in the
distortion transfer function,  dH f , can be assumed constant and hence can be ignored.
Combining eqn 5 and eqn 6 together with the approximation given by eqn 7, yields (see
Appendix),

67
(8)    
2
2
2
0
s
s
b d
i f
c f
dH f e





Using this model, a bank of synthesized signals, corresponding to a range of optional phase
velocity dispersion slope values sb , may be generated by applying the impulse response
function to the reference signal (eqn 8 and eqn 1). The basic phase velocity  0sc f  , can
be approximated by the signal's group velocity which can be measured using a standard
method (e.g. see Wear 2000, eqn. 3). By correlating the distorted signal with the signals in
that bank, the synthesized signal which has the “maximal likelihood” to the measured signal
can be found. Thus, the corresponding phase velocity dispersion slope value sb , for the
object can be determined. This slope is used for characterizing the material.
The Cross Correlation Phase Method
In this section, an alternative method for measuring the dispersion coefficient, sb , using the
cross-correlation function between the reference and the chirp signals which has traveled
through the object is derived.
The term phase-encoded-chirp was introduced by Ha (1996), to denote a chirp which has a
constant phase shift relative to a reference chirp. Ha calculated the approximation to the
cross correlation function between the encoded chirp and the reference chirp to be
proportional to:
(9)  ( ) sinc( )cos 2 cR t BW t f t  
where BW is the chirps' bandwidth, fc is the chirps' central frequency and  is the encoding
phase. The approximation of the cross correlation function is comprised of a sinc envelop
and a carrier frequency fc. According to Ha, in case of a cross correlation between a

68
reference chirp and a phase encoded chirp, the phase of the carrier frequency at the peak of
the sinc envelop (t=0) is equal to the phase between the chirps.
An inspection of eqn. 6, shows that the shape distortion transfer function  dH f adds a
different phase  2 f t f
d
  to every frequency component of the signal. Since the effect
of  dH f is frequency dependent, the distorted signal is not exactly an "encoded signal"
according to Ha's definition. However, Ha's approximation for the cross correlation
function can be used by finding an averaged phase shift angle
(10)  2average df t f       
where f  is the averaged frequency in the signals and  dt f   is the average time
delay of the components in the signal. For a linear frequency modulated chirp the average
frequency is simply the central frequency
(11) cf f 
Using eqn 5 and the narrowband approximation (eqn 7) and the relation
 0s c sd b f c f   yields
(12)  
       
2 2
0 0 0
s s c
d
s s s s
d b f d b fd d
t f
c f c f c f c f
   
    
  
Therefore, the dispersion coefficient bs, can be calculated using equations 10,11 and 12
(13)
 
2
2
0
2
average s
s
c
c f
b
f d



 
Eqn 13 is sufficient for dispersion coefficient measurements in a homogeneous specimen.
However, for medical imaging it is important to study the relation between the phase of the
peak of the cross correlation function and the dispersion in a general object which may be

69
heterogeneous with an unknown thickness. In the more general case, (ignoring the
attenuation) the distortion transfer function is location dependant and can be expressed as,
(14)  
 
0
2 ,
L
di f t f x
dH f e
 

where L denotes the distance from the transmitter at point A to the receiver at point B or the
pulse-echo path along the x direction, and  ,dt f x is the frequency dependent time delay
at that location is
(15)  
   
1 1
,
, 0,
d
s s
t f x dx
c f x c f x
 
     
where  ,sc f x is the phase velocity of frequency f at point x. In a narrowband signal, the
variation of the phase velocity is fairly small compared to the phase velocity and the
following approximation holds,
(16)  
   
 
 
 
2 2
0, ,
,
0, 0,
s s s
d
s s
c f x c f x b x f
t f x dx dx
c f x c f x
   
  
 
Hence,  dH f becomes
(17)  
 
 
2
2
0
2
0,
L
s
s
b x
i f dx
c f x
dH f e


 



 
 
2
0,
s
s
b x
c f x
is a time delay per unit length per unit frequency and is referred herein as
the: “normalized slope” of the phase velocity dispersion. The cumulative normalized slope

70
,
 
 
2
0 0,
L
s
s
b x
dx
c f x


 , in eqn 17 is a projection of the normalized slope of the phase velocity
dispersion along the path from point A to point B through the object or along the traveling
distance of the pulse-echo wave. For a homogeneous object, the cumulative normalized
slope in eqn. 17 is reduced to
(18)
 
   
2
0
20, 0
L
s
s
b db x sdx
c f x c f
s


 

where d is the object's width (as in eqn 8).
The cumulative normalized slope is linearly related to the phase of the peak of the cross
correlation function between the reference and distorted chirps.
(19)
 
 
2
2
0
2
0,
L
s
average c
s
b x
f dx
c f x
 




Using this equation the integrative value (which is actually a projection) of the “normalized
slope” of the phase velocity dispersion is obtained.
Experimental Measurements
The experimental system
The scanning system, utilized to scan a step phantom, is comprised of a water tank with a
specially built computer controlled mechanism that can produce spatial motion with three
degrees of freedom for a pair of transducers (Panametrics, 5 MHz, focused transducers,
diameter 12.7 mm and focal length 10.7cm) placed about twice the focal length apart
(Azhari and Stolarski (1997), Azhari and Sazbon (1999)). In the phase velocity dispersion
slope measurements for a plastic specimen, the transducers were static and the examined
object was placed between them. In the imaging configuration utilized here the object was

71
scanned horizontally. The scanning resolution was set to 0.3mm along the horizontal
direction. Measurements in soft tissue were done in an external water bath with an
unfocused transducer (Panametrics, 5 MHz, diameter 6.3[mm]) placed at a 45 [mm]
distance from a reflecting bronze block.
5800 pulser/receiver was used as a receiver. A Gage CompuScope 12100 (two-channel 50-
MHz or one-channel 100-MHz) 12-bit A/D converter was used to digitally store the
detected waves. A specially built high voltage analog switch was used to isolate the receiver
from the transmission signal in the pulse-echo measurements.
The Studied Specimens
Two specimens were used in this study (i) a plastic step phantom, (ii) a soft tissue (in-
vitro) phantom.
The step phantom (see Fig.1 (a)) was made of polyvinylchloride (PVC). The step size was
2 mm and the minimal thickness was 2 cm. The soft tissue specimens used here was turkey
breast (specimen was obtained from a local commercial slaughterhouse). The soft tissue
specimen was stored in a refrigerator (it was not frozen) and was brought to room
temperature before the experiment. The specimen’s thickness was 45 [mm].
The experimental procedure
Phase velocity cumulative dispersion slope measurement in through transmission:

72
The aim of this part of the experiment was to show that (as predicted by eqns 17,18,19)
the cumulative dispersion slope in the "signals bank" method and the measured angle in
the "cross correlation" method are linearly related to the imaged object width.
A 12s long chirp signal having a 1 MHz bandwidth and a central frequency of
2.5[ ]cf MHz was programmed in the wave generator. Initially, a reference signal of
transmission from one transducer to another in water was recorded. Using this signal, a
distorted signals bank was created. The distorted-signals bank was synthesized using eqns
17,18 for a set of optional cumulative dispersion slope values in the range
 
50 [nano sec]
2
0
b d
s
c f
s


. The velocity  0sc f  was approximated using the method
described by Wear (2000) for group velocity measurement.
In the "imaging configuration" used to scan a polyvinylchloride (PCV), the step phantom
was placed in the water between the two transducers. The signals, sent from one transducer
to another through the phantom were recorded. The recorded signals were analyzed in both
(a) the "signals bank" and (b) the "cross correlation" methods.
For method (a), the recorded signal was correlated with the pre-calculated signals in the
bank of synthesized signals to find the most-likely signal in the bank. The signals were
interpolated using the FFT method (interpft function in Matlab, MathWorks Inc., Natick,
MA) prior the correlation.
Using method (b), the recorded signals were correlated with the reference signal, and the
corresponding angle for every step was calculated from the phases of the cross correlation
functions at their envelopes' peaks. Each phase is the phase of  HR t at its maximal
magnitude, where  HR t is the analytical signal      ˆ
HR t R t iR t  , and  ˆR t is the

73
Hilbert transform of the cross-correlation function between the transmitted and reference
chirp waves.
For both methods the results for each step were plotted against the step width. The results
were also normalized by their corresponding step width and plotted in a different graph for
validation.
Phase velocity dispersion slope measurement in the pulse-echo mode:
The aim of this part in the experiment was to use both methods for measurement of phase
velocity dispersion slope as a function of the frequency for plastic and soft tissue specimens
in the pulse-echo mode.
In the measurement of the dispersion slope using the pulse-echo mode a single transducer
was used for transmission and reception of the signals. The transmitted signals were chirp
signals, 1 MHz bandwidth, 12s long and varying central frequency cf . A  phase
inversion was applied to the echo received from the PVC phantom prior to correlation
calculation. The turkey breast specimen was placed between the transducer and a reflecting
bronze cube. The ultrasonic beam was perpendicular to the tissue fibers direction. The
signals bank was synthesized using eqn 8 for a set of optional values for the dispersion
slope in the ranges 20[ /( )]sb m s MHz  and 2[ /( )]sb m s MHz  for the PVC and
turkey breast phantoms respectively. The recorded signals were analyzed in both (a) the
"signals bank" and (b) the "cross correlation" methods.
For method (a) The recorded signal for each sample and for each central velocity cf , was
correlated with the signals in the bank of synthesized signals to find the most-likely signal

74
in the bank. The signals were interpolated using the FFT method (interpft function in
Matlab) prior the correlation.
For method (b) the recorded signals were correlated with the reference signals. The phase
velocity dispersion slope of the corresponding samples at frequency cf was calculated using
eqn 13.
All experiments were done at room temperature (about 21o
C).
Results
In Fig.1, the results obtained using the measurements of the angle of the peak of the cross
correlation function and the cumulative normalized dispersion slope of the steps of the
PVC step phantom are presented ( 2.5[ ]cf MHz ). Fig.1(a) presents a simple B-Scan image
of the phantom. Fig.1(b) presents the values of the angle of the peak of the cross correlation
function for each step. The error bars present the standard deviation of the measurements
along the steps. Fig.1(c) presents the values of the normalized angle of the peak of the
cross correlation function for each step. The error bars present the standard deviation of the
measurements along the steps. The results for all the steps fell in the range of 0.37±0.01
[rad/cm]. Fig.1(d) shows the cumulative normalized dispersion slope for each step. The
error bars present the standard deviation of the measurements along the steps. In Fig.1(e)
those values are normalized by the steps’ widths. The error bars present the standard
deviation of the measurements along the steps. All values fell in the range of
8.2 0.5[nano sec/cm] .

75
The calculated phase velocity dispersion slope versus cf obtained for the PVC specimen in
the pulse echo mode for the two analysis methods are plotted in Fig 2. The average values
for each central frequency studied are depicted along with their standard deviation values
(error bars). As can be noted, the slope is positive throughout the studied range of
frequencies but decreases monotonically. The values which were calculated using the
signals bank method (Fig2 top) decrease from 5.3 ± 0.9 [m/(sMHz)] at 2 MHz to 2.4 ± 0.4
[m/(sMHz)] at 4.5 MHz. The values which were calculated using the cross correlation
method (Fig2 bottom) decrease from 6.3 ± 1.1 [m/(sMHz)] at 2 MHz to 2.9 ± 0.7
[m/(sMHz)] at 3.75 MHz. As can be noted the results obtained using the cross-correlation
method for frequencies of 4MHz and higher were too scattered and unreliable.
The calculated phase velocity dispersion slope versus cf obtained for the turkey breast in
the pulse echo mode for the two analysis methods are plotted in Fig 3. The average values
for each central frequency studied are depicted along with their standard deviation values
(error bars). As can be noted, the slope is positive throughout the studied range of
frequencies but decreases monotonically. The values which were calculated using the
signals bank method (Fig3 top) decrease from 0.76 ± 0.05 [m/(sMHz)] at 2 MHz to 0.23 ±
0.02 [m/(sMHz)] at 5.5 MHz. The values which were calculated using the cross correlation
method (Fig3 bottom) decrease from 0.64 ± 0.5 [m/(sMHz)] at 2 MHz to 0.25 ± 0.04
[m/(sMHz)] at 5.5 MHz.

76
Discussion
In this study, two new methods for speed of sound dispersion measurement were
developed. To the best of our knowledge, using these methods, speed of sound dispersion
was measured in the pulse-echo mode in soft tissues for the first time.
In the first part of the experiment, it was shown that values of projection measurements in
both methods are linearly related with the width of the measured object and therefore both
methods are suitable for projection imaging.
In the second part of the experiment, the feasibility of performing measurements in pulse-
echo mode was confirmed. Although the results obtained here for the PVC specimen are
similar to those obtained using a different method (Levy et al. 2006), the results obtained
here for the turkey breast specimen are smaller than those reported there. This stems from
the fact that in this study the ultrasonic beam was perpendicular to the tissue fibers whereas
in the other study it was done along with fibers orientation. This finding is consistent with
the phenomenon reported for the myocardium by Marutyan et al. (2006). They have
reported that the speed sound and SOSD change substantially with the orientation of the
myofibers. Their findings indicate that SOSD along the myofibers is more than twice the
SOSD perpendicular to the myofibers.
Although both methods presented here are based on transmission of the same signal, they
are very different. The signals bank method is a robust method which performs better in
low SNR cases (see Fig.2). This method can be used with any signal shape and with any
sound velocity model. It can be shown that in the narrowband approximation and for a chirp
signal, this method is similar to wavelet analysis of a scaled mother wavelet, where the
mother wavelet is the reference signal (Similar to Bilgen 1999). Using more complicated
sound velocity model may offer the ability for conducting measurements in a wideband.

77
Ignoring the attenuation does not degrade the reliability of the results of this method, yet, in
this method, the attenuation response of the measured object may be incorporated in the
overall transfer response function using eqn 6. On the other hand, the computational effort
during the data analysis in this method is large (required several seconds of computation on
a PC per transmitted signal). The cross correlation method is an elegant fast (about two
orders of magnitude shorter computation time) measurement technique based on
approximations and averaging. Therefore it is valid only for narrowband measurements and
it may be biased by frequency dependent attenuation.
Acknowledgments
We are grateful for funding provided by the Galil Center For Telemedicine and Medical
Informatics and by the Technion V.P.R. Research Funds, Eliyahu Pen Research Fund, Dent
Charitable Trust, Japan Technion Society and the Montréal Biomedical Fund.
Finally, we thank Mr. Aharon Alfasi for his extremely valuable technical support.
APPENDIX
Using eqn 5
(A.1)  
   
   
   
0
0 0
s s
d
s s s s
c f c fd d
t f d
c f c f c f c f
 
   
  
.
and the narrowband approximation (eqn 7)

78
(A.2)  
        
       0 0
s c s c s s c s
d
s s s s
c f b f c f b f f b f
t f d d
c f c f c f c f
     
  
   
.
Assuming weak dispersion (i.e.  0s sd b f c f   ),  dt f can be approximated by
(A.3)  
 
2
0
s
d
s
b f
t f d
c f

 

.

79
References
Feb;30(1):35-48.
1999;212(1):270-275.
Bhatia KG, Singh VR. Ultrasonic characteristics of leiomyoma uteri in vitro. Ultrasound
Med Biol. 2001;27:983-987.
Bilgen M, Wavelet Transform-Based Strain Estimator for Elastography. IEEE transactions
on ultrasonics, ferroelectrics, and frequency control 1999;46(6):1407-1416
Carstensen EL, Measurement of Dispersion of Velocity of Sound in Liquids. J. Accoust.
Soc. Am 1954;26:858-861.
Greenleaf JF. Tissue Characterization with Ultrasound. Boca Raton, FL CRC Press, 1986.
Ha STT, Zhou H, Sheriff RE and McDonald JA, Fourier transform approximations for
sweeps and phase-encoded sweeps. GEOPHYSICS, 1996;61(4):1440–1452.
He P. Experimental Verification of Models for Determining Dispersion from Attenuation.
Levy Y, Agnon Y and Azhari H. Measurement of Speed of Sound Dispersion in Soft
Tissues Using a Double Frequency Continuous Wave Method UMB 2006;32(7):1065-
1071.
Mamou J, Oelze ML, O Brien WD , Zachary JF. Perspective on Biomedical Quantitative
Ultrasound Imaging. IEEE SIGNAL PROCESSING MAGAZINE 2006;May:112-116

80
Manoharan A, Chen CF, Wilson LS, Griffiths KA, Robinson DE. Ultrasonic
characterization of splenic tissue in myelofibrosis: further evidence for reversal of fibrosis
with chemotherapy. European-journal-of-haematology 1988;40:149-154.
Marutyan RK, Yang M, Baldwin SL, Wallace KD, Holland MR, And Miller JG. The
Frequency Dependence of Ultrasonic Velocity And The Anisotropy Of Dispersion In Both
Freshly Excised And Formalin-Fixed Myocardium. Ultrasound Med Biol. 2006; 32(4):603–
610.
Wear KA, A numerical method to predict the effects of frequency dependent attenuation
and dispersion on speed of sound estimates in cancellous bone. J. Acoust. Soc. Am.
2001;109 (3):1213-1218.
Wells P N T, Ultrasonic imaging of the human body. Rep. Prog. Phys. 1999;62:671-722.

81
Figure captions.
Figure 1: (a) A B-scan image of the scanned stepped PVC phantom. (b) The angle obtained
by the cross-correlation method for each step. (c) The angles shown in (b) normalized by
the step thickness. (d) The cumulative normalized dispersion slope obtained for each step of
the phantom. (e) The values of (d) normalized to the thickness of each step.
Figure 2: (Top) The dispersion slope values as a function of frequency obtained by the
pulse-echo mode and the “signals bank” method in PVC. (Bottom) The dispersion slope
values as a function of frequency obtained by the pulse-echo mode and the “cross-
correlation” method.
Figure 3: (Top) The dispersion slope values as a function of frequency obtained by the
pulse-echo mode and the “signals bank” method in a turkey breast specimen. (Bottom) The
dispersion slope values as a function of frequency obtained by the pulse-echo mode and the
“cross-correlation” method.

85
Paper D: "Velocity Measurements Using a Single Transmitted Linear Frequency
Modulated Chirp"
Abstract
Velocity measurement is a challenge for a variety of remote sensing systems such as
ultrasonic and radar scanners. However, current Doppler-based techniques require a
comparatively long data acquisition time. It has been suggested to use coded signals, such
as linear frequency modulated signals (chirp), for ultrasonic velocity estimation by
extracting the needed information from a set of several sequential coded pulses. In this
study a method for velocity estimation using a single linear frequency modulated chirp
transmission is presented and implemented for ultrasonic measurements. The complex cross
correlation function between the transmitted and reflected signals is initially calculated. The
velocity is then calculated from the phase of the peak of the envelop of this cross
correlation function. The suggested method was verified using computer simulations and
experimental measurements in an ultrasonic system. Applying linear regression to the data
has yielded very good correlation (R=0.989). With the suggested technique higher frame
rates of velocity mapping can be potentially achieved relative to current techniques. Also,
the same data can be utilized for both velocity mapping and image reconstruction.
Key Words: Velocity measurement, Coded excitation, Linear frequency modulated chirp.

86
Introduction
Measurement of velocity is a challenge for a variety of remote sensing systems such as
ultrasonic and radar scanners. Commonly, the Doppler frequency shift caused by a moving
reflector is measured and converted into velocity estimation. This method is well
established and has been implemented using many techniques. However, current Doppler-
based techniques require either the transmission of a long continuous wave, which
sacrifices axial resolution, or the acquisition of echoes from several pulses to generate a
velocity map of each region in the image. Therefore, both methods require a comparatively
long data acquisition time, typically on the order of the period of the Doppler frequency
shift.
Coded excitation methodology (Misaridis and Jensen 2005) is used in ultrasonic imaging
systems to improve signal to noise ratio (SNR). In this methodology, a long coded signal is
used to transmit high energy while preserving low intensity constraints. While typically a
long pulse duration leads to poor spatial resolution, using coded excitations the high spatial
resolution can be recovered using an appropriate signal processing algorithm (e.g., matched
filter (Misaridis and Jensen 2005)). It has been suggested to use coded signals, such as
linear frequency modulated signals (chirp), for ultrasonic velocity estimation by extracting
the needed information from a set of several sequential coded pulses (Wilhjelm and
Pedersen 1993).
In this study we present a method for velocity estimation using a single coded pulse
transmission.

87
Theory
A chirp from f0 to f1 whose length is Tm can be represented by the following formula
(Jensen1996, eqn 9.20)
   2
0 0sin 2 ;0 me t f t S t t T     (1)
where f0 is the start frequency, f1 is the end frequency and S0 is the sweep rate of the signal
( 1 0
0
m
f f
S
T

 ).
The instantaneous frequency of the signal is (Wilhjelm and Pedersen 1993)
  0 0f t f S t  . (2)
The time of appearance of each frequency  t f is
  0
0
f f
t f
S

 . (3)
Other properties of the chirp signal are
1 0f f f   (4)
1 0
2
m
f f
f

 (5)
where f is the frequency bandwidth of the chirp and fm is the center instantaneous
frequency.
A received signal  sr t from a moving reflector with a velocity v along the beam axis can
be represented by (Jensen 1996, eqn 9.21)
   'sr t a e t t
c v
c v


  



(6)
where a is a reflection coefficient (a frequency independent reflection is assumed), c is the
acoustic velocity in the medium and t' is a time shift that is related to the path from the
transducer to the moving target. The signal's intensity is not important in the following
discussion, therefore, we set a = 1.
When c >> 2v

Yoav Levy PHD Thesis - innovative techniques for US imaging

Yoav Levy PHD Thesis - innovative techniques for US imaging

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